{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "pULeWpb_V1an"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Preparing the data"
      ],
      "metadata": {
        "id": "B0UF-zsdN3GH"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.linspace(0, 10*np.pi, num=1000)\n",
        "e = np.random.normal(scale=10.0, size=x.size)\n",
        "y = 65.0 + 1.8*x + 40*np.cos(x) + e"
      ],
      "metadata": {
        "id": "PRRbdnKxN4dI"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(x, y);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "3dWuxcybOk6Q",
        "outputId": "1a2aea49-06cd-4c4f-b828-a1b3a254681f"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# PyTorch gradient calculation example\n",
        "\n",
        "Useful docs from the official documentation:\n",
        "\n",
        "https://pytorch.org/tutorials/beginner/blitz/autograd_tutorial.html\n",
        "\n",
        "https://pytorch.org/tutorials/beginner/introyt/autogradyt_tutorial.html\n",
        "\n",
        "https://pytorch.org/tutorials/beginner/basics/tensorqs_tutorial.html"
      ],
      "metadata": {
        "id": "jNaHTljDRGKv"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import torch"
      ],
      "metadata": {
        "id": "wsiB75RyMU4P"
      },
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "xt = torch.tensor(x)\n",
        "yt = torch.tensor(y)\n",
        "learning_rate = 1e-2"
      ],
      "metadata": {
        "id": "JcyZUYI0OXK5"
      },
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(xt, yt);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "LuniuOf8V8__",
        "outputId": "403a184c-842d-4399-a06b-e72b890228c3"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## A simple linear regression model\n",
        "w = torch.tensor(1.0, requires_grad=True)\n",
        "b = torch.tensor(1.0, requires_grad=True)\n",
        "def model(x):\n",
        "    return w * x + b\n",
        "\n",
        "## Compute prediction error\n",
        "def loss_fn(prediction, y):\n",
        "    return ((prediction-y)**2).mean()\n",
        "\n",
        "prediction = model(xt)\n",
        "loss = loss_fn(prediction, yt)\n",
        "\n",
        "## Backpropagation\n",
        "loss.backward()\n",
        "with torch.no_grad():\n",
        "    w -= w.grad * learning_rate\n",
        "    b -= b.grad * learning_rate\n",
        "    # Set the gradients to zero\n",
        "    w.grad.zero_()\n",
        "    b.grad.zero_()\n"
      ],
      "metadata": {
        "id": "WGz_QYCROWe2"
      },
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w, b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aMwng0ckOvWW",
        "outputId": "e4c4f60e-9ef6-4f16-d6f8-bf4af378e3ed"
      },
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(tensor(26.2882, requires_grad=True), tensor(2.5240, requires_grad=True))"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# TensorFlow gradient calculation example\n",
        "\n",
        "Useful docs from the official documentation:\n",
        "\n",
        "https://www.tensorflow.org/guide/basic_training_loops\n",
        "\n",
        "https://www.tensorflow.org/guide/autodiff\n",
        "\n",
        "https://www.tensorflow.org/api_docs/python/tf/Variable\n",
        "\n",
        "https://www.tensorflow.org/api_docs/python/tf/Tensor"
      ],
      "metadata": {
        "id": "7SxnMNRwSjf-"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import tensorflow as tf"
      ],
      "metadata": {
        "id": "DBElUY4ASjIu"
      },
      "execution_count": 9,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "xt = tf.constant(x, dtype=tf.float32)\n",
        "yt = tf.constant(y, dtype=tf.float32)\n",
        "learning_rate = 1e-2"
      ],
      "metadata": {
        "id": "WUrhNNynTcWg"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(xt, yt);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "cLghBObMembw",
        "outputId": "78e38991-1f0f-47de-abf9-6066e12cc346"
      },
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "## A simple linear regression model\n",
        "w = tf.Variable(1.0, trainable=True)\n",
        "b = tf.Variable(1.0, trainable=True)\n",
        "def model(x):\n",
        "    return w * x + b\n",
        "\n",
        "## Compute prediction error\n",
        "def loss_fn(prediction, y):\n",
        "    return tf.reduce_mean(tf.square(prediction-y))\n",
        "\n",
        "with tf.GradientTape() as tape:\n",
        "    prediction = model(xt)\n",
        "    loss = loss_fn(prediction, yt)\n",
        "\n",
        "## Backpropagation\n",
        "dw, db = tape.gradient(loss, [w, b])\n",
        "w.assign_sub(learning_rate * dw)\n",
        "b.assign_sub(learning_rate * db);"
      ],
      "metadata": {
        "id": "kGZL525ESnAk"
      },
      "execution_count": 12,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "w, b"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "peAH3R0jWuZb",
        "outputId": "e6514177-d886-4d65-aa82-3dc0b10fa658"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(<tf.Variable 'Variable:0' shape=() dtype=float32, numpy=26.28819>,\n",
              " <tf.Variable 'Variable:0' shape=() dtype=float32, numpy=2.5239797>)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "# JAX gradient calculation example\n",
        "\n",
        "Useful docs from the official documentation:\n",
        "\n",
        "https://jax.readthedocs.io/en/latest/jax-101/01-jax-basics.html\n",
        "\n",
        "https://jax.readthedocs.io/en/latest/jax-101/04-advanced-autodiff.html"
      ],
      "metadata": {
        "id": "jzVhN5FPReOo"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import jax\n",
        "import jax.numpy as jnp"
      ],
      "metadata": {
        "id": "zeEW8C9oWLoe"
      },
      "execution_count": 14,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "xt = jnp.array(x)\n",
        "yt = jnp.array(y)\n",
        "learning_rate = 1e-2"
      ],
      "metadata": {
        "id": "l4sLSnR6PEmp",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "28bf471f-a11d-401b-cb23-3ae633a25beb"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "WARNING:jax._src.xla_bridge:No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(x, y);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 430
        },
        "id": "8z_jnIoXRnze",
        "outputId": "66e9dc6d-693e-48b1-9d1a-87b6a48e8f0a"
      },
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# A simple linear regression model\n",
        "model_parameters = jnp.array([1., 1.])\n",
        "def model(theta, x):\n",
        "    w, b = theta\n",
        "    return w * x + b\n",
        "\n",
        "# Function to compute prediction error\n",
        "def loss_fn(model_parameters, x, y):\n",
        "    prediction = model(model_parameters, x)\n",
        "    return jnp.mean((prediction-y)**2)\n",
        "\n",
        "# Backpropagation\n",
        "grads_fn = jax.grad(loss_fn)\n",
        "grads = grads_fn(model_parameters, xt, yt)\n",
        "model_parameters -= learning_rate * grads"
      ],
      "metadata": {
        "id": "PvNR9aWpV_jG"
      },
      "execution_count": 17,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "model_parameters"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "OAVmXbc0O_dC",
        "outputId": "83d741bc-e53b-4910-c9d7-d16dd7541bab"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Array([26.288193 ,  2.5239797], dtype=float32)"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "oMiX5_S_ZOBm"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}